# An Optimization-Based System Dynamics Simulation for Sustainable Policy Design in WEEE Management Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optimization-Based Simulation for WEEE Management

#### 2.1. Reverse Logistics Process

- Acquisition: is the inflow of the system, which consists of consolidating and repurchasing used products, components or materials.
- Collection: is the process that moves products from the acquisition points to inspection/sorting facilities.
- Inspection and sorting: consists of evaluating the general appearance and condition of the products. After inspection, the returned goods go to either the processing stage or are diverted to an export process for treatment and disposition abroad [3].
- Processing: includes different practices such as renovation through the repair and/or replacement of damaged parts, disassembly for cannibalization through the use of its components in different products, recycling for obtaining raw materials such as gold, silver, etc., and finally, elimination/deactivation for the proper final disposal of probably hazardous materials.
- Disposition: is the final reintroduction of the products in an appropriated channel or market depending on the previous treatment. These markets include the following: remanufactured markets for second-hand products, component markets resulting from cannibalization and recycled materials markets. If there are no more possibilities of waste profiting, disposal is the final option.

#### 2.2. System Dynamics Model

#### 2.3. Optimization Model

#### 2.3.1. Objective Function

#### 2.3.2. Constraints

#### 2.3.3. Environmental Indicator (Alternative Objective Function)

#### 2.4. OBS Implementation

- Estimate WEEE generation. Initially, at the beginning of each cycle, SD is used to estimate the effect of several repurchase prices and its corresponding generation of WEEE according to the dynamics of the market described in Section 2.2. This procedure updates the values used in the piecewise linear approximation of the optimization model (Equations (26)–(32)) and in the GRAPH function for the WEEE generation process of the SD model (Equation (20)). In this step, we test iteratively increasing values of $pr$ (beginning at a given value $p{p}_{0}$ equal to 0) and store the corresponding values of q.
- Run the optimization model. Using the previous estimates, in this step, the optimization model (of Section 2.3) chooses the optimal point for the repurchase price ($pr$) and its corresponding generation of WEEE (q). Simultaneously, the optimization model also specifies the flow entering the RL process x and the flows inside it (variables $v,y$ and w), as well as the capacities of the different stages (variables z).
- Simulate the WEEE management system. At this step, the SD model (Section 2.2) considers the output of the optimization model and uses the Euler integration method to model the interaction between flows and levels of the WEEE management system (${D}_{E},{S}_{E},{C}_{E},S{t}_{E},D{i}_{W},{G}_{W}$). At the WEEE generation level (${G}_{W}$), the simulation uses again the estimates of the piecewise linear approximation ($Pl,{Q}_{l},l\in PL$) and represents the WEEE management level (${M}_{W}$) with the RL processes inside it. The SD model runs under these conditions for a period of $\tau $ weeks. Once the reoptimization period ($\tau $) is reached, the procedure runs step 1 for a new WEEE generation estimate and step 2 for a reoptimization of the RL process.
- Report performance metrics. Once the simulation horizon (T) is reached, four different performance metrics of the system are reported: (i) the total profit, (ii) the total AEB, (iii) the total number of units of WEEE processed by the WEEE management system and (iv) the average repurchase price.

## 3. Results and Discussion

#### 3.1. Case Study: Colombian Mobile Phones

#### 3.2. Optimization-Based Optimization Benefits

#### Environmental vs. Economic Optimization Comparison

#### 3.3. Scenario Analysis

#### 3.3.1. Treatment Alternatives Scenario

#### 3.3.2. Processing Capacity Impact

#### 3.3.3. MPs Frequency of Replacement Effect

#### 3.3.4. Customer Repurchase Price Expectations

## 4. Conclusions and Perspectives

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABS | Agent-based simulation |

AEB | Avoided environmental burden |

DES | Discrete-event simulation |

EEE | Electric and electronic equipment |

MINLP | Mixed-integer nonlinear program |

MP | Mobile phone |

OBS | Optimization-based simulation |

RL | Reverse logistics |

SD | System dynamics |

WEEE | Waste of electric and electronic equipment |

WMP | Waste mobile phone |

## Appendix A. Model Notation

#### Appendix A.1. System Dynamics Notation

${D}_{E}$: | Demand of EEE |

${S}_{E}$: | Supply of EEE |

${C}_{E}$: | Circulation of EEE |

$S{t}_{E}$: | Storage of EEE |

${G}_{W}$: | Generation of WEEE |

${M}_{W}$: | Management of WEEE |

$pch$: | Purchase of EEE |

$sl$: | Sale of EEE |

$pper$: | Per person |

$mkn$: | Marketing of new EEE |

$mks$: | Marketing of second-hand EEE |

$rsg$: | Rate of supply growth |

$rm$: | Remanufactured EEE |

$eqa$: | EEE available for sale |

$nd$: | New demand of EEE |

$ctm$: | Customers |

$rcg$: | Rate of customers growth |

$di$: | Disposal |

$rd$: | Rate of disposal |

$dw$: | Disposition of WEEE |

$out$: | Output of accumulated EEE |

$rpl$: | EEE replaced |

$tm$: | Time of replacement |

$rr$: | Rate of replacement |

$vrr$: | Initial value of replacement rate |

$epp$: | Effect of purchase price |

$fp$: | Function price |

$pp$: | Average purchase price |

$pne$: | Average price of new EEE |

$rdi$: | Potential disposal rate |

$vrdi$: | Initial value of disposal rate |

$ei$: | Incentive effect |

$fi$: | Function incentive |

$pr$: | Repurchase price |

$aq$: | Acquisition |

$ra$: | Rate of acquisition |

$ciepd$: | Collection, inspection or export, processing and disposition |

#### Appendix A.2. Optimization

Sets | |

$RL$: | Stages of the RL process |

A: | Acquisition process |

R: | Collection process |

F: | Inspection and sorting process |

$Ex$: | Export option |

$TR$: | Treatment or processing options $p\in TR=\{elimination/deactivation,recycling,$ $disassembly,renovation\}$ |

C: | Market alternatives $mC=\{export,disposal,recycled\phantom{\rule{0.166667em}{0ex}}materials,component,$ $second$-$hand\phantom{\rule{3.33333pt}{0ex}}products\}$ |

$T{E}_{i}$: | {1,…$O{p}_{s}$} where $O{p}_{s}$ is the number of technology options i for each stage $s\in RL$ |

$RL$: | {A} ∪ {R} ∪ {F} ∪ {$Ex$} ∪ {$TR$} |

$PL$: | Number of segments of the piecewise linear approximation for the generation of WEEE based on the volume q to price $pr$ relationship |

#### Appendix A.2.1. Parameters

${Q}_{l}$: | Generation of WEEE in point $l\in PL$ |

${P}_{l}$: | Repurchase price in point $l\in PL$ |

$Cex$: | Variable export cost |

$C{p}_{k}$: | Variable costs of treatment processes $k\in TR$ |

$G{r}_{i}$: | Fixed costs of technology option i for collection process |

$G{f}_{i}$: | Fixed costs of technology option i for inspection process |

$Ge{x}_{i}$: | Fixed costs of technology option i for export |

$G{p}_{i}^{k}$: | Fixed costs of technology option i for treatment process k |

$H{r}_{i}$: | Capacity of technology i for the collection process |

$H{f}_{i}$: | Capacity of technology i for the inspection process |

$He{x}_{i}$: | Capacity of alternative i for the export option |

$H{p}_{i}^{k}$: | Capacity of technology i for treatment process $k\in TR$ |

${B}_{m}$: | Avoided environmental burden (AEB) of each market alternative $m\in C$ |

$Ae{x}_{i}$: | AEB percentage obtained with option i of the export alternative |

$A{p}_{i}^{k}$: | AEB percentage obtained with technology i of the treatment process $k\in TR$ |

$S{p}_{k}$: | Proportion of the WEEE flow that can be treated in process $k\in TR$ according to its entering status |

$S{c}_{k,m}$: | Percentage of the WEEE that can flow to each market alternative $m\in C$ according to the treatment process $k\in TR$ |

${I}_{m}$: | Revenues generated by each market alternative $m\in C$ |

${D}_{m}$: | Maximum demand for each market alternative $m\in C$ |

$Mr$: | Minimum percentage collection policy to ensure flow entering the WEEE management system |

#### Appendix A.2.2. Decision Variables

x: | Amount of WEEE acquired and entering the RL process |

${\lambda}_{l}$: | Weight of point l in $PL$ |

${b}_{l}$: | Binary variable; 1 if interval between points l and $l+1$ is activated in the piecewise linear approximation, 0 otherwise |

q: | Amount of WEEE generated |

$pr$: | Repurchase price |

${v}_{f}$: | Flow of WEEE that enters the inspection and sorting process |

${v}_{ex}$: | Flow of WEEE exported |

${y}_{k}$: | Flow of WEEE that goes to treatment process $k\in TR$ |

${w}_{m}$: | Flow of valorized WEEE placed in market $m\in C$ |

$z{r}_{i}$: | Binary variable; 1 if technology i is chosen for the collection process, 0 otherwise |

$z{f}_{i}$: | Binary variable; 1 if technology i is chosen for the inspection and sorting process, 0 otherwise |

$ze{x}_{i}$: | Binary variable; 1 if option i is chosen for the export, 0 otherwise |

$z{p}_{i}^{k}$: | Binary variable; 1 if technology i is chosen for treatment process $k\in TR$, 0 otherwise |

## References

- Cucchiella, F.; D’Adamo, I.; Lenny Koh, S.C.; Rosa, P. Recycling of WEEEs: An economic assessment of present and future e-waste streams. Renew. Sustain. Energy Rev.
**2015**, 51, 263–272. [Google Scholar] [CrossRef][Green Version] - Mihai, F.C.; Gnoni, M.G.; Meidiana, C.; Ezeah, C.; Elia, V. Waste Electrical and Electronic Equipment (WEEE): Flows, Quantities, and Management—A Global Scenario. In Electronic Waste Management and Treatment Technology; Elsevier: Amsterdam, The Netherlands, 2019; pp. 1–34. [Google Scholar]
- Ilankoon, I.M.S.K.; Ghorbani, Y.; Chong, M.N.; Herath, G.; Moyo, T.; Petersen, J. E-waste in the international context–A review of trade flows, regulations, hazards, waste management strategies and technologies for value recovery. Waste Manag.
**2018**, 82, 258–275. [Google Scholar] [CrossRef] - Galeano, D.A.R.; Rodríguez, S.C.B. An integrated method of environmental analysis and system dynamics for management of mobile phone waste in Colombia. J. Clean. Prod.
**2021**, 279, 123768. [Google Scholar] [CrossRef] - Ardi, R.; Leisten, R. Assessing the role of informal sector in WEEE management systems: A System Dynamics approach. Waste Manag.
**2016**, 57, 3–16. [Google Scholar] [CrossRef] [PubMed] - Kaya, M. Recovery of metals and nonmetals from electronic waste by physical and chemical recycling processes. Waste Manag.
**2016**, 57, 64–90. [Google Scholar] [CrossRef] [PubMed] - Zhang, L.; Xu, Z. A review of current progress of recycling technologies for metals from waste electrical and electronic equipment. J. Clean. Prod.
**2016**, 127, 19–36. [Google Scholar] [CrossRef] - Forti, V.; Balde, C.P.; Kuehr, R.; Bel, G. The Global E-waste Monitor 2020: Quantities, Flows and the Circular Economy Potential. United Nations University. 2020. Available online: http://ewastemonitor.info/ (accessed on 13 October 2021).
- Zeng, X.; Duan, H.; Wang, F.; Li, J. Examining environmental management of e-waste: China’s experience and lessons. Renew. Sustain. Energy Rev.
**2017**, 72, 1076–1082. [Google Scholar] [CrossRef] - De Souza, R.G.; Clímaco, J.C.N.; Sant’Anna, A.P.; Rocha, T.B.; do Valle, R.d.A.B.; Quelhas, O.L.G. Sustainability assessment and prioritisation of e-waste management options in Brazil. Waste Manag.
**2016**, 57, 46–56. [Google Scholar] [CrossRef][Green Version] - Salhofer, S.; Steuer, B.; Ramusch, R.; Beigl, P. WEEE management in Europe and China—A comparison. Waste Manag.
**2016**, 57, 27–35. [Google Scholar] [CrossRef] - Achillas, C.; Vlachokostas, C.; Aidonis, D.; Moussiopoulos, N.; Iakovou, E.; Banias, G. Optimising reverse logistics network to support policy-making in the case of Electrical and Electronic Equipment. Waste Manag.
**2010**, 30, 2592–2600. [Google Scholar] [CrossRef] - Achillas, C.; Vlachokostas, C.; Moussiopoulos, N.; Perkoulidis, G.; Banias, G.; Mastropavlos, M. Electronic waste management cost: A scenario-based analysis for Greece. Waste Manag. Res.
**2014**, 29, 963–972. [Google Scholar] [CrossRef] [PubMed] - Dias, P.; Machado, A.; Huda, N.; Bernardes, A.M. Waste electric and electronic equipment (WEEE) management: A study on the Brazilian recycling routes. J. Clean. Prod.
**2018**, 174, 7–16. [Google Scholar] [CrossRef] - Perkins, D.N.; Drisse, M.N.B.; Nxele, T.; Sly, P.D. E-waste: A global hazard. Ann. Glob. Health
**2014**, 80, 286–295. [Google Scholar] [CrossRef] - Temur, G.T.; Bolat, B. Evaluating efforts to build sustainable WEEE reverse logistics network design: Comparison of regulatory and non-regulatory approaches. Int. J. Sustain. Eng.
**2017**, 10, 358–383. [Google Scholar] [CrossRef] - Sepúlveda, A.; Schluep, M.; Renaud, F.G.; Streicher, M.; Kuehr, R.; Hagelüken, C.; Gerecke, A.C. A review of the environmental fate and effects of hazardous substances released from electrical and electronic equipments during recycling: Examples from China and India. Environ. Impact Assess. Rev.
**2010**, 30, 28–41. [Google Scholar] [CrossRef] - D’Adamo, I.; Ferella, F.; Gastaldi, M.; Maggiore, F.; Rosa, P.; Terzi, S. Towards sustainable recycling processes: Wasted printed circuit boards as a source of economic opportunities. Resour. Conserv. Recycl.
**2019**, 149, 455–467. [Google Scholar] [CrossRef] - Li, X.; Mu, D.; Du, J.; Cao, J.; Zhao, F. Game-based system dynamics simulation of deposit-refund scheme for electric vehicle battery recycling in China. Resour. Conserv. Recycl.
**2020**, 157, 104788. [Google Scholar] [CrossRef] - Alumur, S.A.; Nickel, S.; Saldanha-da Gama, F.; Verter, V. Multi-period reverse logistics network design. Eur. J. Oper. Res.
**2012**, 220, 67–78. [Google Scholar] [CrossRef] - Agrawal, S.; Singh, R.K.; Murtaza, Q. A literature review and perspectives in reverse logistics. Resour. Conserv. Recycl.
**2015**, 97, 76–92. [Google Scholar] [CrossRef] - Agarwal, G.; Barari, S.; Tiwari, M.K. A PSO-based optimum consumer incentive policy for WEEE incorporating reliability of components. Int. J. Prod. Res.
**2012**, 50, 4372–4380. [Google Scholar] [CrossRef] - Sterman, J.D. Business Dynamics: Systems Thinking and Modeling for a Complex World; McGraw-Hill: New York, NY, USA, 2000. [Google Scholar]
- Topcu, A.; Benneyan, J.C.; Cullinane, T.P. A simulation-optimisation approach for reconfigurable inventory space planning in remanufacturing facilities. Int. J. Bus. Perform. Supply Chain. Model.
**2013**, 5, 86–114. [Google Scholar] [CrossRef] - Joshi, B.V.; Vipin, B.; Ramkumar, J.; Amit, R. Impact of policy instruments on lead-acid battery recycling: A system dynamics approach. Resour. Conserv. Recycl.
**2021**, 169, 105528. [Google Scholar] [CrossRef] - Matsumoto, M. Development of a simulation model for reuse businesses and case studies in Japan. J. Clean. Prod.
**2010**, 18, 1284–1299. [Google Scholar] [CrossRef] - Pandian, G.R.S.; Abdul-Kader, W. Performance evaluation of reverse logistics enterprise—An agent-based simulation approach. Int. J. Sustain. Eng.
**2017**, 10, 384–398. [Google Scholar] [CrossRef][Green Version] - Gamberini, R.; Gebennini, E.; Manzini, R.; Ziveri, A. On the integration of planning and environmental impact assessment for a WEEE transportation network—A case study. Resour. Conserv. Recycl.
**2010**, 54, 937–951. [Google Scholar] [CrossRef] - Govindan, K.; Soleimani, H.; Kannan, D. Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future. Eur. J. Oper. Res.
**2015**, 240, 603–626. [Google Scholar] [CrossRef][Green Version] - Lahane, S.; Kant, R.; Shankar, R. Circular Supply Chain Management: A State-of-art review and future opportunities. J. Clean. Prod.
**2020**, 258, 120859. [Google Scholar] [CrossRef] - Georgiadis, P.; Besiou, M. Sustainability in electrical and electronic equipment closed-loop supply chains: A system dynamics approach. J. Clean. Prod.
**2008**, 16, 1665–1678. [Google Scholar] [CrossRef] - Georgiadis, P.; Besiou, M. Environmental and economical sustainability of WEEE closed-loop supply chains with recycling: A system dynamics analysis. Int. J. Adv. Manuf. Technol.
**2010**, 47, 475–493. [Google Scholar] [CrossRef] - Guo, Q.; Wang, E.; Nie, Y.; Shen, J. Profit or environment? A system dynamic model analysis of waste electrical and electronic equipment management system in China. J. Clean. Prod.
**2018**, 194, 34–42. [Google Scholar] [CrossRef][Green Version] - Rodríguez-Bello, L.A.; Estupiñán-Escalante, E. The impact of waste of electrical and electronic equipment public police in Latin America: Analysis of the physical, economical, and information flow. In Handbook of Electronic Waste Management; Elsevier: Amsterdam, The Netherlands, 2020; pp. 397–419. [Google Scholar]
- Mashhadi, A.R.; Behdad, S.; Zhuang, J. Agent Based Simulation Optimization of Waste Electrical and Electronics Equipment Recovery. J. Manuf. Sci. Eng.
**2016**, 138, 101007. [Google Scholar] [CrossRef][Green Version] - Ghisolfi, V.; Diniz Chaves, G.d.L.; Ribeiro Siman, R.; Xavier, L.H. System dynamics applied to closed loop supply chains of desktops and laptops in Brazil: A perspective for social inclusion of waste pickers. Waste Manag.
**2017**, 60, 14–31. [Google Scholar] [CrossRef] - Yao, L.; Liu, T.; Chen, X.; Mahdi, M.; Ni, J. An integrated method of life-cycle assessment and system dynamics for waste mobile phone management and recycling in China. J. Clean. Prod.
**2018**, 187, 852–862. [Google Scholar] [CrossRef] - Xue, R.; Zhang, F.; Tian, F. A system dynamics model to evaluate effects of retailer-led recycling based on dual chains competition: A case of e-waste in China. Sustainability
**2018**, 10, 3391. [Google Scholar] [CrossRef][Green Version] - Elia, V.; Gnoni, M.G.; Tornese, F. Designing a sustainable dynamic collection service for WEEE: An economic and environmental analysis through simulation. Waste Manag. Res.
**2019**, 37, 402–411. [Google Scholar] [CrossRef] [PubMed] - Shokohyar, S.; Mansour, S. Simulation-based optimisation of a sustainable recovery network for Waste from Electrical and Electronic Equipment (WEEE). Int. J. Comput. Integr. Manuf.
**2013**, 26, 487–503. [Google Scholar] [CrossRef] - Coyle, R.G. The use of optimization methods for policy design in a system dynamics model. Syst. Dyn. Rev.
**1985**, 1, 81–91. [Google Scholar] [CrossRef] - Dangerfield, B.; Roberts, C. An overview of strategy and tactics in system dynamics optimization. J. Oper. Res. Soc.
**1996**, 47, 405–423. [Google Scholar] [CrossRef] - Xu, J.; Li, X. Using system dynamics for simulation and optimization of one coal industry system under fuzzy environment. Expert Syst. Appl.
**2011**, 38, 11552–11559. [Google Scholar] [CrossRef] - Wu, Z.; Xu, J. Predicting and optimization of energy consumption using system dynamics-fuzzy multiple objective programming in world heritage areas. Energy
**2013**, 49, 19–31. [Google Scholar] [CrossRef] - Li, T.; Yang, S.; Tan, M. Simulation and optimization of water supply and demand balance in Shenzhen: A system dynamics approach. J. Clean. Prod.
**2019**, 207, 882–893. [Google Scholar] [CrossRef] - Figueira, G.; Almada-Lobo, B. Hybrid simulation-optimization methods: A taxonomy and discussion. Simul. Model. Pract. Theory
**2014**, 46, 118–134. [Google Scholar] [CrossRef][Green Version] - Dangerfield, B.; Duggan, J. Optimization of system dynamics models. In System Dynamics: Theory and Applications; Springer: Berlin/Heidelberg, Germany, 2020; pp. 139–152. [Google Scholar]
- De Brito, M.P.; Dekker, R. A framework for reverse logistics. In Reverse Logistics; Springer: Berlin/Heidelberg, Germany, 2004; pp. 3–27. [Google Scholar]
- Islam, M.T.; Huda, N. Reverse logistics and closed-loop supply chain of Waste Electrical and Electronic Equipment (WEEE)/E-waste: A comprehensive literature review. Resour. Conserv. Recycl.
**2018**, 137, 48–75. [Google Scholar] [CrossRef] - Diaz, A.; Alvarez, M.; Gonzalez, P. Logistica Inversa y Medio Ambiente; McGraw-Hill: Madrid, Spain, 2004; p. 353. [Google Scholar]
- Williams, H.P. Model Building in Mathematical Programming; John Wiley & Sons: Hoboken, NJ, USA, 2013. [Google Scholar]
- Nelen, D.; Manshoven, S. A multidimensional indicator set to assess the benefits of WEEE material recycling. J. Clean. Prod.
**2014**, 83, 305–316. [Google Scholar] [CrossRef][Green Version] - Oswald, I. Environmental Metrics for WEEE Collection and Recycling Programs. Ph.D. Thesis, Universitat Augsburg, Augsburg, Germany, 2013. [Google Scholar]
- Mason, A.J. OpenSolver-An open source add-in to solve linear and integer progammes in Excel. In Operations Research Proceedings 2011; Springer: Berlin/Heidelberg, Germany, 2012; pp. 401–406. [Google Scholar]
- Belotti, P. Couenne: A User’s Manual. 2009. Available online: https://www.coin-or.org/Couenne/couenne-user-manual.pdf (accessed on 13 October 2021).
- Czyzyk, J.; Mesnier, M.P.; Moré, J.J. The NEOS Server. IEEE J. Comput. Sci. Eng.
**1998**, 5, 68–75. [Google Scholar] [CrossRef] - Seref, M.M.; Ahuja, R.K.; Winston, W.L. Developing Spreadsheet-Based Decision Support Systems; Dynamic Ideas: Charlestown, MA, USA, 2007. [Google Scholar]
- Ministerio de Ambiente y Desarrollo Sostenible. Programa Posconsumo—Información General. Available online: https://www.minambiente.gov.co/index.php/component/content/article/28-plantilla-asuntos-ambientales-y-sectorial-y-urbana (accessed on 13 October 2021).
- Meloan, M.; Castells, P. Country Overview: Colombia; Technical Report; GSM Association: London, UK, 2017. [Google Scholar]
- Magalini, F.; Kuehr, R.; Baldé, C. eWaste en América Latina: Análisis Estadístico y Recomendaciones de Política Pública; Technical Report; United Nations University: Tokyo, Japan, 2015. [Google Scholar]
- World Bank. Mobile Cellular Subscriptions (per 100 People)—Colombia. 2018. Available online: https://datos.bancomundial.org/indicator/IT.CEL.SETS.P2?locations=CO&name_desc=fals (accessed on 13 October 2021).
- Redondo, J.M.; Ibarra-Vega, D.; Monroy, L.; Bermúdez, J. Assessment strategies for the integral management of waste electrical and electronic equipment-WEEE. Dyna
**2018**, 85, 319–327. [Google Scholar] [CrossRef] - Deloitte. Consumo Movil en Colombia; Technical Report; Deloitte Touche Tohmatsu Limited: London, UK, 2017. [Google Scholar]
- Belmont Trading. Personal Communication: Commercial Proposal for Academic Use. 2018. Available online: https://www.belmont-trading.com/colombia/ (accessed on 13 October 2021).
- Intex Mundi. Precious Materials Prices. 2018. Available online: https://www.indexmundi.com/es/precios-de-mercado/ (accessed on 13 October 2021).
- Hischier, R.; Wager, P.; Gauglhofer, J. Does WEEE recycling make sense from an environmental perspective? The environmental impacts of the Swiss take-back and recycling systems for waste electrical and electronic equipment (WEEE). Environ. Impact Assess. Rev.
**2015**, 25, 525–539. [Google Scholar] [CrossRef] - Martinez-Moyano, I.J.; Richardson, G.P. Best practices in system dynamics modeling. Syst. Dyn. Rev.
**2013**, 29, 102–123. [Google Scholar] [CrossRef] - Gollakota, A.R.; Gautam, S.; Shu, C.M. Inconsistencies of e-waste management in developing nations–Facts and plausible solutions. J. Environ. Manag.
**2020**, 261, 110234. [Google Scholar] [CrossRef] - Ben Yahya, T.; Jamal, N.M.; Sundarakani, B.; Omain, S.Z. Factors Affecting Mobile Waste Recycling through RSCM: A Literature Review. Recycling
**2021**, 6, 30. [Google Scholar] [CrossRef] - Cruz-Sotelo, S.E.; Ojeda-Benítez, S.; Jauregui Sesma, J.; Velázquez-Victorica, K.I.; Santillán-Soto, N.; García-Cueto, O.R.; Alcantara Concepcion, V.; Alcántara, C. E-waste supply chain in Mexico: Challenges and opportunities for sustainable management. Sustainability
**2017**, 9, 503. [Google Scholar] [CrossRef][Green Version] - Echegaray, F.; Hansstein, F.V. Assessing the intention-behavior gap in electronic waste recycling: The case of Brazil. J. Clean. Prod.
**2017**, 142, 180–190. [Google Scholar] [CrossRef] - Tan, Q.; Duan, H.; Liu, L.; Yang, J.; Li, J. Rethinking residential consumers’ behavior in discarding obsolete mobile phones in China. J. Clean. Prod.
**2018**, 195, 1228–1236. [Google Scholar] [CrossRef] - Arya, S.; Kumar, S. E-waste in India at a glance: Current trends, regulations, challenges and management strategies. J. Clean. Prod.
**2020**, 271, 122707. [Google Scholar] [CrossRef]

Point | $\mathit{pr}$ | q | Weight $\left({\mathit{\lambda}}_{\mathit{l}}\right)$ | Intervals $\left(\mathit{l}\right)$ | $\left({\mathit{b}}_{\mathit{l}}\right)$ |
---|---|---|---|---|---|

0 | 0 | 466 | ${\lambda}_{1}$ | 1 | ${b}_{1}$ |

1 | 50 | 530 | ${\lambda}_{2}$ | 1 and 2 | ${b}_{1},{b}_{2}$ |

2 | 100 | 597 | ${\lambda}_{3}$ | 2 and 3 | ${b}_{2},{b}_{3}$ |

3 | 150 | 641 | ${\lambda}_{4}$ | 3 and 4 | ${b}_{3},{b}_{4}$ |

4 | 200 | 670 | ${\lambda}_{5}$ | 4 and 5 | ${b}_{4},{b}_{5}$ |

5 | 250 | 701 | ${\lambda}_{6}$ | 5 | ${b}_{5}$ |

Variables | Description/Input Data | Source |
---|---|---|

Marketing of EEE | Weekly growth rate of EEE supply: 0.070% | [32,59,60] |

Purchase of EEE | Weekly growth rate of EEE demand: 0.064% | [32,61] |

Replacement of EEE | Potential weekly replacement rate of EEE: 0.077% Frequency of purchase of a new EEE: every 74 weeks | [62,63] |

Repurchase price | Monetary incentive and willingness to dispose their EEE | [35] |

Management of WEEE | RL process costs, revenues and environmental impact for each stage and market | [12,52,64,65,66] |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Llerena-Riascos, C.; Jaén, S.; Montoya-Torres, J.R.; Villegas, J.G. An Optimization-Based System Dynamics Simulation for Sustainable Policy Design in WEEE Management Systems. *Sustainability* **2021**, *13*, 11377.
https://doi.org/10.3390/su132011377

**AMA Style**

Llerena-Riascos C, Jaén S, Montoya-Torres JR, Villegas JG. An Optimization-Based System Dynamics Simulation for Sustainable Policy Design in WEEE Management Systems. *Sustainability*. 2021; 13(20):11377.
https://doi.org/10.3390/su132011377

**Chicago/Turabian Style**

Llerena-Riascos, Camilo, Sebastián Jaén, Jairo Rafael Montoya-Torres, and Juan G. Villegas. 2021. "An Optimization-Based System Dynamics Simulation for Sustainable Policy Design in WEEE Management Systems" *Sustainability* 13, no. 20: 11377.
https://doi.org/10.3390/su132011377